One of the reasons that Apollo 13 safely returned was due to a Texhnical Note written in 1959 by Barbara J. Short entitled. Point Return Landings From the Moon to the Eartth
This gave the equations needed for trajectory and burn rates
I will raise my glass to John Houbolt.
Cheers.
Thank you for sharing your insights.
North American Aviation in Downey, CA designed the Mercury, Gemini, Apollo and Shuttle rockets. Santa Susana near Chatsworth, CA is a hilly spot with scaffolding to test all the engines. When I asked my father why Apollo 13 was a miracle, he told me that the three astronauts were the best pilots in the country and the Commander, Jim Lovell, was given a most difficult assignment: to pass through the atmosphere at the right angle in order to not get burned up. How tight was the angle? A few degrees. How did Lovell hit it? Perfectly with pure courage, excellent piloting skills and probably a little grace from God.
My father was an engineer for the Navaho. Insiders will know how that rocket triggered the Kennedy speech and NASA. He told me that the basic mathematics for orbiting was taken from Rene Descartes (1596-1650). Shows us the brilliance of French mathematicians.
By the way, the average age of the engineers for the sixteen Apollo missions was 25. The astronauts were always the oldest members of the team at 35. Very humbling.
A good book on the American space industry is William Mellberg, Moon Missions (1997).
http://amzn.com/1882663128